Answer:
$91.07
Step-by-step explanation:
You cannot take off 9.8% from $100 to find the answer, since 9.8% of $100 is more tax than she will pay. The toy has to cost less than $100, so that when you add 9.8% tax the price you end up with exactly $100, and 9.8% of under $100 is less that 9.8% of $100. Maybe this is why you are a few cents off.
This is how you do it.
The price of the toy is unknown, so we'll cal it x.
When you add 9.8% tax to x, you want to end up with exactly $100.
x + 9.8% of x = 100
Write 9.8% as a decimal by dividing the percent by 100.
9.8% = 9.8/100 = 0.098
Now we have:
x + 0.098x = 100
Add like terms on the left side:
1.098x = 100
Divide both sides by 1.098:
x = 100/1.098
x = 91.07
Answer: The most expensive toy she can get costs $91.07 before tax.
Check:
We now add 9.8% tax to $91.07 and make sure the total cost including tax is no more than $100.
$91.07 + 9.8% of $91.07 =
= $91.07 + 0.098 * $91.07
= $91.07 + $8.92
= $99.99
It seems that you could try to spend one more cent, to really get to the $100 limit, so let's try $91.08 as the most expensive toy she can buy.
We now add 9.8% tax to $91.08 and see what the total cost including tax is.
$91.08 + 9.8% of $91.08 =
= $91.08 + 0.098 * $91.08
= $91.08 + $8.93
= $100.01
You see that if Megan gets a $91.08 toy, with tax, the total cost is $100.01, which is over the $100 limit, so the answer is indeed $91.07.
